Woohoo -- the book is finished!
Of course, now we have all the lessons that haven't yet been put in the book. The website has downloads of several lessons. I haven't printed them out yet. But still, it's exciting.
As to why I haven't been giving much description of what's been going on with RightStart Geometry, well, it's because I've had less and less to do with it. Kid1 deals with it all pretty much on her own. I deal a little with the fallout, such as when she paused too long between lessons and apparently forgot how to do basic trig (much weeping and gnashing of teeth that week). And occasionally she would ask me a question....
Wow, did it ever reach the point where I couldn't answer questions, since I hadn't been following along. Yes, I can do trig, but I'm not really tip-of-the-tongue with it. I would stare blankly at whatever diagram she was showing me ("Mommy, I need to know this interior section of this pyramid so I can compare it to this cone" -- ick, I just remembered that I did dislike parts of math back in school, particularly anything to do with cones). And the answer sheets don't really go step by step through the logic of solving the problem. Or maybe they do, but not in enough detail for me -- I want them to explain it like Mr. Broman did years ago in high school trig, and the answer sheets are more like that TA in that Saturday morning math class freshman year at Purdue.
Also, one memorable occasion I used the phrase "well, you need to isolate x on one side", and, gees, you'd have thought I'd announced she needed to sacrifice her firstborn on a flaming pyre. "That's algebra! I don't know algebra!" Um, yes, you just did it in all of these problems up here without realizing it.
All of which is leading me to consider what to do next -- what program will we try once all of this is done. I'm factoring in her flair for drama about math concepts she doesn't instantly comprehend, as well as my dislike of cones. Where do we go from here?
Showing posts with label RightStart. Show all posts
Showing posts with label RightStart. Show all posts
16 October 2007
22 August 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
(I think we have skipped some lessons here in my chronicle of our time with RightStart. I suspect Kid1 did them last June and I never got around to commenting on them.)
Lesson131 Basic Trigonometry
Day one:
I am not prepared to be “back to school”, but Kid1 has decided to bustle around doing school this morning. Her resolve to get into the school groove starts to crumble as she reads through the RightStart explanation of trigonometry. I read through it -- it’s thorough and succinct. I help her through the first problem, finding sine, cosine and tangent of a 45 degree right triangle, showing my work on the chalkboard (I love doing math on a chalkboard -- whiteboards just don’t cut it for the tactile satisfaction). Her eyes are glazed, she keeps asking why, as in why the heck would anyone DO this? I suggest we drop it for today and try a different approach tomorrow.
Day two:
I have googled various websites on the uses of trigonometry, trying to choose ones that will interest her. She is unimpressed. Next we get out Zaccaro’s Challenge Math and read through the chapter on trigonometry in it. I point out the exciting concept that triangles can be different sizes yet have the same ratio of opposite side/adjacent side. She rolls her eyes at this -- it is such old news. But she starts to realize that this isn’t some weird new branch of math someone dreamed up just to torment innocent young students -- this is a logical outgrowth of things she already knows.
We look at a few of the word problems in Challenge Math but decide against doing them. I like the way RightStart approaches trig better, mostly because it’s the way I learned trig many years ago.
Day three:
Ready to tackle the RightStart worksheet again. We work through the sine, cosine and tangent of a 30-60 triangle together, using the chalkboard. Then she starts filling the The Chart -- it’s a chart of sine, cosine and tangent of 5 degrees, 10 degrees, 15 degrees, etc. on up to 85 degrees. She is to measure triangles on the second worksheet, then use her measurements for her calculations. No indication is given whether it would be better to measure in metric or inches, but she decides metric would be more accurate.
I am on alert, since I’ve noticed that this business of measuring can turn into disaster -- sometimes the reproduction of the worksheets is a scootchy bit off, leading to different interpretations of length. Since she’s going to be using millimeters to calculate, she could rapidly end up with an answer that’s fairly different from what it should be (especially since she’s to use the table she’s making for the next lesson). We hit on a strategy -- first of all, I look at the answer sheet and discover that every hypotenus is 10 centimeters. Aha -- I figured there would be some constant somewhere, since that’s the way elementary math books tend to work. Plus “10” is easy to divide by, so it makes oodles of sense that every hypotenus would be ten.
I keep the answer sheet out. She measures the sides of each triangle, then tells me what she gets for the measurement. I tell her what the answer sheet says. We quickly ponder the difference (can she see why they called it what they did?), then she uses the “official measure” for her calculations. I draw traingles on the chalkboard for her and label the angles and sides with A,B,C,a,b,c. She soon sees the patterns that are forming with her answers (which is why it’s so cool to do this exercise, and why I wanted to do it instead of just doing the Chalenge Math -- you can discover the relationships between sine, cosine and tangents of the various angles as you calculate them).
The lesson took 3 days and plenty of parental involvement, but in the end she is confident that trigonometry is something she can deal with.
Lesson 132 Solving Trig Problems
Kid1 zips through this lesson, using the chart of trig ratios from lesson 131. She feels good about this.
The discussion of Problem 1 comments that “your answer may not quite agree with the solution. Trig ratios cannot be calculated very accurately by measuring as you did.” Umm, I feel like we’ve been caught cheating on yesterday’s chart!
Lesson 133 Comparing Calculators
MrV’s scientific calculator uses Reverse Polish Notation, so I decide to spring for the calculator specified in the book instead of making do with his. I bought our Casio fx300MS from Amazon since our local Target didn’t have it and I was able to get free shipping (driving around town looking for one was going to use up as much gas as the price differential).
It looks rather like a Star Trek data pad, which makes it a very satisfying addition to our household. The kids quickly figured out how to use it. Kid1 didn’t make it all the way through the worksheet, though, as she started feeling woozy, heralding a fever. She'll get back to this lesson after she recovers.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
(I think we have skipped some lessons here in my chronicle of our time with RightStart. I suspect Kid1 did them last June and I never got around to commenting on them.)
Lesson131 Basic Trigonometry
Day one:
I am not prepared to be “back to school”, but Kid1 has decided to bustle around doing school this morning. Her resolve to get into the school groove starts to crumble as she reads through the RightStart explanation of trigonometry. I read through it -- it’s thorough and succinct. I help her through the first problem, finding sine, cosine and tangent of a 45 degree right triangle, showing my work on the chalkboard (I love doing math on a chalkboard -- whiteboards just don’t cut it for the tactile satisfaction). Her eyes are glazed, she keeps asking why, as in why the heck would anyone DO this? I suggest we drop it for today and try a different approach tomorrow.
Day two:
I have googled various websites on the uses of trigonometry, trying to choose ones that will interest her. She is unimpressed. Next we get out Zaccaro’s Challenge Math and read through the chapter on trigonometry in it. I point out the exciting concept that triangles can be different sizes yet have the same ratio of opposite side/adjacent side. She rolls her eyes at this -- it is such old news. But she starts to realize that this isn’t some weird new branch of math someone dreamed up just to torment innocent young students -- this is a logical outgrowth of things she already knows.
We look at a few of the word problems in Challenge Math but decide against doing them. I like the way RightStart approaches trig better, mostly because it’s the way I learned trig many years ago.
Day three:
Ready to tackle the RightStart worksheet again. We work through the sine, cosine and tangent of a 30-60 triangle together, using the chalkboard. Then she starts filling the The Chart -- it’s a chart of sine, cosine and tangent of 5 degrees, 10 degrees, 15 degrees, etc. on up to 85 degrees. She is to measure triangles on the second worksheet, then use her measurements for her calculations. No indication is given whether it would be better to measure in metric or inches, but she decides metric would be more accurate.
I am on alert, since I’ve noticed that this business of measuring can turn into disaster -- sometimes the reproduction of the worksheets is a scootchy bit off, leading to different interpretations of length. Since she’s going to be using millimeters to calculate, she could rapidly end up with an answer that’s fairly different from what it should be (especially since she’s to use the table she’s making for the next lesson). We hit on a strategy -- first of all, I look at the answer sheet and discover that every hypotenus is 10 centimeters. Aha -- I figured there would be some constant somewhere, since that’s the way elementary math books tend to work. Plus “10” is easy to divide by, so it makes oodles of sense that every hypotenus would be ten.
I keep the answer sheet out. She measures the sides of each triangle, then tells me what she gets for the measurement. I tell her what the answer sheet says. We quickly ponder the difference (can she see why they called it what they did?), then she uses the “official measure” for her calculations. I draw traingles on the chalkboard for her and label the angles and sides with A,B,C,a,b,c. She soon sees the patterns that are forming with her answers (which is why it’s so cool to do this exercise, and why I wanted to do it instead of just doing the Chalenge Math -- you can discover the relationships between sine, cosine and tangents of the various angles as you calculate them).
The lesson took 3 days and plenty of parental involvement, but in the end she is confident that trigonometry is something she can deal with.
Lesson 132 Solving Trig Problems
Kid1 zips through this lesson, using the chart of trig ratios from lesson 131. She feels good about this.
The discussion of Problem 1 comments that “your answer may not quite agree with the solution. Trig ratios cannot be calculated very accurately by measuring as you did.” Umm, I feel like we’ve been caught cheating on yesterday’s chart!
Lesson 133 Comparing Calculators
MrV’s scientific calculator uses Reverse Polish Notation, so I decide to spring for the calculator specified in the book instead of making do with his. I bought our Casio fx300MS from Amazon since our local Target didn’t have it and I was able to get free shipping (driving around town looking for one was going to use up as much gas as the price differential).
It looks rather like a Star Trek data pad, which makes it a very satisfying addition to our household. The kids quickly figured out how to use it. Kid1 didn’t make it all the way through the worksheet, though, as she started feeling woozy, heralding a fever. She'll get back to this lesson after she recovers.
06 June 2007
A Good Poem About Ten!
Okay, as much as I like RightStart overall, I think that "Yellow Is the Sun" poem for teaching what makes ten is abysmal. Really. It's nonsense.
BUT!
I just found this at David Darcy's blog. So clever! I think I'm going to teach it to my kids, even though we're already past that stage in math. Well, some days Kid2 is sort of wobbly on What Makes Ten, but we're theoretically past it...do you really ever get past What Makes Ten, really? Hmmm....
Actually, I just discovered David Darcy's blog, via a link in ... hmm ... someone else's blog ... dang, I was so excited about the Ten Poem I lost track of who it was, so I can't link them. Sorry. Anyway, I'm off to uncover other gems.
BUT!
I just found this at David Darcy's blog. So clever! I think I'm going to teach it to my kids, even though we're already past that stage in math. Well, some days Kid2 is sort of wobbly on What Makes Ten, but we're theoretically past it...do you really ever get past What Makes Ten, really? Hmmm....
Actually, I just discovered David Darcy's blog, via a link in ... hmm ... someone else's blog ... dang, I was so excited about the Ten Poem I lost track of who it was, so I can't link them. Sorry. Anyway, I'm off to uncover other gems.
15 May 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 125 Pick’s Theorem With the Stomachion
Another chance to integrate math with other subjects! The Stomachion appears on one of Archimedes manuscripts. Although a brief history of Archimedes and the Stomachion is in the book, homeschool moms who are on-the-ball might consider reading more about Archimedes at this time. As for me, not being particularly on-the-ball, I waited until this week to look up Archimedes and the Door to Science at the local library and discovered every single copy is currently checked out AND there’s a waiting list of holds.
We looked at some Internet information on the Stomachion, using the site that is given in the RightStart book. We clicked on some of the links and discovered a page a page in which some of the information was given in Latin with no translation. Kid1 was intrigued, and read it all aloud, but gave no indication of how much she actually understood.
Lesson 126 Pick’s Theorem and Pythagorean Theorem
“That was easy.”
(Puts RightStart book back on shelf.)
“I really like Pick’s Theorem.”
As a matter of fact, some math-based discussion came up over the weekend while we were visiting aunts and uncles. I heard her comment, “that’s like Pick’s theorem,” at one point. She’s thinking about this stuff way beyond school time!
Lesson 127 Estimating Area With Pick’s Theorem
“The size of wildfires are calculated by using this method.” Well, who knew?
I am amazed that this lesson is completed with no griping whatsoever. She enjoys working with this. Later I realize that she didn’t do the final problem, that of using Pick’s theorem and a map of our state to find the area of our state. I am pretty sure this doesn't matter, given that she understands the concept.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 125 Pick’s Theorem With the Stomachion
Another chance to integrate math with other subjects! The Stomachion appears on one of Archimedes manuscripts. Although a brief history of Archimedes and the Stomachion is in the book, homeschool moms who are on-the-ball might consider reading more about Archimedes at this time. As for me, not being particularly on-the-ball, I waited until this week to look up Archimedes and the Door to Science at the local library and discovered every single copy is currently checked out AND there’s a waiting list of holds.
We looked at some Internet information on the Stomachion, using the site that is given in the RightStart book. We clicked on some of the links and discovered a page a page in which some of the information was given in Latin with no translation. Kid1 was intrigued, and read it all aloud, but gave no indication of how much she actually understood.
Lesson 126 Pick’s Theorem and Pythagorean Theorem
“That was easy.”
(Puts RightStart book back on shelf.)
“I really like Pick’s Theorem.”
As a matter of fact, some math-based discussion came up over the weekend while we were visiting aunts and uncles. I heard her comment, “that’s like Pick’s theorem,” at one point. She’s thinking about this stuff way beyond school time!
Lesson 127 Estimating Area With Pick’s Theorem
“The size of wildfires are calculated by using this method.” Well, who knew?
I am amazed that this lesson is completed with no griping whatsoever. She enjoys working with this. Later I realize that she didn’t do the final problem, that of using Pick’s theorem and a map of our state to find the area of our state. I am pretty sure this doesn't matter, given that she understands the concept.
09 May 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 124 Pick’s Theorem
A geoboard is optional for this lesson, although it certainly makes life easier, since Pick’s theorem has to do with using a grid. We have geoboards because we’ve done so many levels of RightStart. And I’d like to pause here and say that I really, really do not like the geoboards: I bought a geoboard directly from RightStart, and it doesn’t match the pictures in the RightStart books (the grid has fewer pegs, which sometime makes the problems in the RightStart book impossible to replicate). Also, the rubber bands drive me nuts; this is not RightStart's fault, though, as it is simply a function of geoboards and the deterioration of rubber bands.
Kid1 reported, though, that the size of the geoboard does not matter for this lesson. Frankly, she breezed through it so quickly that I’m not sure much of anything mattered. The lesson also requires remembering how to find the area of polygons, with references given to previous lessons for those who don’t remember how. Kid1 obviously remembers how.
This is the only RightStart lesson she’s done all week because we’ve been working on Challenge Math, in which we’ve worked with decimals. For the record, Kid1 reports that she will never, ever forget how to do long division with decimals now, having slogged through all of those problems (by the way, for those who have never looked at Challenge Math, it is mainly story problems).
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 124 Pick’s Theorem
A geoboard is optional for this lesson, although it certainly makes life easier, since Pick’s theorem has to do with using a grid. We have geoboards because we’ve done so many levels of RightStart. And I’d like to pause here and say that I really, really do not like the geoboards: I bought a geoboard directly from RightStart, and it doesn’t match the pictures in the RightStart books (the grid has fewer pegs, which sometime makes the problems in the RightStart book impossible to replicate). Also, the rubber bands drive me nuts; this is not RightStart's fault, though, as it is simply a function of geoboards and the deterioration of rubber bands.
Kid1 reported, though, that the size of the geoboard does not matter for this lesson. Frankly, she breezed through it so quickly that I’m not sure much of anything mattered. The lesson also requires remembering how to find the area of polygons, with references given to previous lessons for those who don’t remember how. Kid1 obviously remembers how.
This is the only RightStart lesson she’s done all week because we’ve been working on Challenge Math, in which we’ve worked with decimals. For the record, Kid1 reports that she will never, ever forget how to do long division with decimals now, having slogged through all of those problems (by the way, for those who have never looked at Challenge Math, it is mainly story problems).
01 May 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 123 Napoleon’s Theorem
The lesson starts with a brief history lesson (I didn’t realize that Napoleon was an amateur mathematician).
Then, on to the theorem itself: “If equilateral traingles are constructed on the outside of the three sides of any given triangle, then their centroids are the vertices of ....” Well, surprise! You get to figure it out for yourself.
Up to this point in RightStart Geometry, equilateral triangles have been constructed using a T-square and 30-60 triangle. Now we learn how to make an equilateral triangle with a compass (the mmArc compass).
The end of the lesson discusses generalizing -- first, what does it mean to generalize, then, what happens when we generalize about non-equilateral triangles.
Lesson 124 is about Pick’s theorem. Kid1 opened the book to it, looked it over, and asked if we could spend some time on Challenge Math instead. We’ve been working with decimals in Challenge Math for the past several days -- we’ll return to Pick’s theorem eventually.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 123 Napoleon’s Theorem
The lesson starts with a brief history lesson (I didn’t realize that Napoleon was an amateur mathematician).
Then, on to the theorem itself: “If equilateral traingles are constructed on the outside of the three sides of any given triangle, then their centroids are the vertices of ....” Well, surprise! You get to figure it out for yourself.
Up to this point in RightStart Geometry, equilateral triangles have been constructed using a T-square and 30-60 triangle. Now we learn how to make an equilateral triangle with a compass (the mmArc compass).
The end of the lesson discusses generalizing -- first, what does it mean to generalize, then, what happens when we generalize about non-equilateral triangles.
Lesson 124 is about Pick’s theorem. Kid1 opened the book to it, looked it over, and asked if we could spend some time on Challenge Math instead. We’ve been working with decimals in Challenge Math for the past several days -- we’ll return to Pick’s theorem eventually.
24 April 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 119 More Golden Goodies
Although Lesson 118 took Kid1 several hours, leaving me filled with dread for this whole Golden Ratio study, this lesson is done quietly and relatively quickly.
One worksheet is simply drawing the golden spiral that can be made by dividing a rectangle into a rectangle-plus-square. So. Cool. I would’ve thought this was one of the coolest math lessons ever if I were a kid doing it. And Kid1 seems to catch the charm.
Golden triangles are also discussed, which are less charming, but not too bad.
Lesson 120 Fibonacci Sequence
“If you ever played the ‘Chain’ games, you will recognize the ones column as a chain.” What are “Chain” games? Should I know this?
Much drawing on the worksheets, which have graph paper on them to help with the drawing. Lots of little bricks and stair steps. I think it’s all great fun. Kid1 doesn’t share my enthusiasm.
The final paragraph asks kids to make up their own Fibonacci problem. “If you think of a good one, let me know at joancotter[rest of email address]”. I think that’s a great touch -- asking the kids to get in touch with the author and share their ideas. Kid1 has no interest in it, of course. Oh well -- someone out there will enjoy it!
Lesson 1221 Fibonacci Numbers and Phi
“Fibonacci spirals are found in the seed heads of dandelions, daisies, and sunflowers.” Enchanting idea, but the second worksheet isn't quite so arty and poetic as this blurb makes Fibonacci sequences sound. It it based on the work of Robert Dimson, the Scottish mathematician. I am called upon to help interpret fn x fn + 2 along with (fn + 1)squared. Once Kid1 sees someone else talk through it, she’s okay with it. She doesn’t even blink at tackling the final problems, which look like: (fn x fn + 2) - (fn + 1)squared = 1 (the question being, is that true when n is even, or when n is odd?).
Lesson 122 Golden Ratios and Other Ratios Around Us
More history of the Golden Ratio, then a chance to run around the house measuring various things. I am asked the dimensions of a legal pad (8.5 by 14) and the television (no clue, you’ll have to measure it yourself).
The worksheet also has questions about the ratios of the 30-60 triangle and the 45 triangle that are used in the course.
The whole thing is accomplished without grumbling and without announcements of how many more lessons are left in the book.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 119 More Golden Goodies
Although Lesson 118 took Kid1 several hours, leaving me filled with dread for this whole Golden Ratio study, this lesson is done quietly and relatively quickly.
One worksheet is simply drawing the golden spiral that can be made by dividing a rectangle into a rectangle-plus-square. So. Cool. I would’ve thought this was one of the coolest math lessons ever if I were a kid doing it. And Kid1 seems to catch the charm.
Golden triangles are also discussed, which are less charming, but not too bad.
Lesson 120 Fibonacci Sequence
“If you ever played the ‘Chain’ games, you will recognize the ones column as a chain.” What are “Chain” games? Should I know this?
Much drawing on the worksheets, which have graph paper on them to help with the drawing. Lots of little bricks and stair steps. I think it’s all great fun. Kid1 doesn’t share my enthusiasm.
The final paragraph asks kids to make up their own Fibonacci problem. “If you think of a good one, let me know at joancotter[rest of email address]”. I think that’s a great touch -- asking the kids to get in touch with the author and share their ideas. Kid1 has no interest in it, of course. Oh well -- someone out there will enjoy it!
Lesson 1221 Fibonacci Numbers and Phi
“Fibonacci spirals are found in the seed heads of dandelions, daisies, and sunflowers.” Enchanting idea, but the second worksheet isn't quite so arty and poetic as this blurb makes Fibonacci sequences sound. It it based on the work of Robert Dimson, the Scottish mathematician. I am called upon to help interpret fn x fn + 2 along with (fn + 1)squared. Once Kid1 sees someone else talk through it, she’s okay with it. She doesn’t even blink at tackling the final problems, which look like: (fn x fn + 2) - (fn + 1)squared = 1 (the question being, is that true when n is even, or when n is odd?).
Lesson 122 Golden Ratios and Other Ratios Around Us
More history of the Golden Ratio, then a chance to run around the house measuring various things. I am asked the dimensions of a legal pad (8.5 by 14) and the television (no clue, you’ll have to measure it yourself).
The worksheet also has questions about the ratios of the 30-60 triangle and the 45 triangle that are used in the course.
The whole thing is accomplished without grumbling and without announcements of how many more lessons are left in the book.
17 April 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 116 Cross Multiplying on the Multiplication Table
I didn’t realize there was a term for this idea of cross-multiplying. What it refers to is looking at a multiplication table for 1x6 and 3x2; now, if you draw a line between the 1 on the first line and the 6 on the second line (showing you’re multiplying them), then draw a line between the 2 on the second line and the 3 on the first line (showing you’re multiplying them), you’ve made a big X.
Various applications are given. For example, mental multiplication can sometimes be easier with cross-multiplication: 8x35 forms a cross with (and therefore has the same answer as) 20x14. (I’ve gotta admit, though, I would never, ever mentally multiply 8x35 that way...I might factor it out a bit and make it 40x7, but probably I’d just do 8x30 plus 8x5 and move on with my life; however, MrV is much quicker at mental math than I, and I wonder if he’s using this technique at times.) Another application is in simplifying proportions.
Lesson 117 Measuring Heights
You know, if I weren’t reviewing every single lesson in this Appleworks file, I might never have realized that this lesson called for a small mirror and a sunny day. Yoohoo, that didn’t happen around here -- no mirrors or sunny days were used to measure the height of something tall outside (tree, pole, building). Hmmm.
Lesson 118 Golden Ratio
KidV1 despised this lesson, and managed to spend the entire day on it. Really, it’s just a matter of calculating phi to a couple of digits, then working with it a bit. It’s hard for me to help her, as her worksheet it so covered with doodles that I can barely see the problems.
Among the issues: she announces that she likes the “other rectangles” better than those that are golden rectangles. She finds them more pleasing. Sigh. How to explain centuries of design theory in about 5 minutes and (possibly) motivate her? I explain that the ancient Greeks used the Golden Ratio in their architecture (she’s currently fascinated with the Greeks), I google pictures of buildings both ancient and modern, I find a page on web design that explains how to use Golden Rectangles to make customer-pleasing design, we look at phi to 1000 decimal places (weird numbers are also interesting). In the end, though, it’s just a matter of “This Must Be Done. Period.”
Really, she has great talent for engineering and architecture, so it’s annoying that she hates this so. I console myself with the thought that perhaps she’ll be a groundbreaking designer that will find a new proportion that will revolutionize design theory.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 116 Cross Multiplying on the Multiplication Table
I didn’t realize there was a term for this idea of cross-multiplying. What it refers to is looking at a multiplication table for 1x6 and 3x2; now, if you draw a line between the 1 on the first line and the 6 on the second line (showing you’re multiplying them), then draw a line between the 2 on the second line and the 3 on the first line (showing you’re multiplying them), you’ve made a big X.
Various applications are given. For example, mental multiplication can sometimes be easier with cross-multiplication: 8x35 forms a cross with (and therefore has the same answer as) 20x14. (I’ve gotta admit, though, I would never, ever mentally multiply 8x35 that way...I might factor it out a bit and make it 40x7, but probably I’d just do 8x30 plus 8x5 and move on with my life; however, MrV is much quicker at mental math than I, and I wonder if he’s using this technique at times.) Another application is in simplifying proportions.
Lesson 117 Measuring Heights
You know, if I weren’t reviewing every single lesson in this Appleworks file, I might never have realized that this lesson called for a small mirror and a sunny day. Yoohoo, that didn’t happen around here -- no mirrors or sunny days were used to measure the height of something tall outside (tree, pole, building). Hmmm.
Lesson 118 Golden Ratio
KidV1 despised this lesson, and managed to spend the entire day on it. Really, it’s just a matter of calculating phi to a couple of digits, then working with it a bit. It’s hard for me to help her, as her worksheet it so covered with doodles that I can barely see the problems.
Among the issues: she announces that she likes the “other rectangles” better than those that are golden rectangles. She finds them more pleasing. Sigh. How to explain centuries of design theory in about 5 minutes and (possibly) motivate her? I explain that the ancient Greeks used the Golden Ratio in their architecture (she’s currently fascinated with the Greeks), I google pictures of buildings both ancient and modern, I find a page on web design that explains how to use Golden Rectangles to make customer-pleasing design, we look at phi to 1000 decimal places (weird numbers are also interesting). In the end, though, it’s just a matter of “This Must Be Done. Period.”
Really, she has great talent for engineering and architecture, so it’s annoying that she hates this so. I console myself with the thought that perhaps she’ll be a groundbreaking designer that will find a new proportion that will revolutionize design theory.
11 April 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 111 Sierpinski Triangle
Introduces much history of geometry -- Euclid and the Elements, Benoit Mandelbrot and The Fractal Geometry of Nature, and , of course, Waclaw Sierpinski and The Sierpinski Triangle. I don’t know if Kid1 caught the point of all of this history -- I wouldn’t have at her age. Then again, she has a more subtle mind than I (this isn’t saying much).
The worksheets ask for three iterations of the Sierpinski Triangle.
Lesson 112 Koch Snowflake
We both hit a snag on worksheet 1. Kid1 is able to easily draw iterations of the Koch Snowflake, but the algorithm to figure out the perimeter escapes her. She is able to graph out what will happen to the permimeter and area -- the “analysis” section of the book pretty much lays that out -- but doesn’t get how to put the perimeters into numbers. I peek at the answers. I discover that each perimeter is to be multiplied by 4/3 to find the next iteration. Well, how the heck would I have known that? I’m totally clueless as to how we were supposed to figure that out. Really. The only thing I can think of is that the Sierpinski Triangle in lesson 111 had each iteration shaded 3/4 more, so maybe those numbers should’ve been on my mind? Huh? I should email RightStart and ask them.
Lesson 113 Cotter Tens Fractal
Yes, it’s the fractal we all know and love from Level B and/or Transitions -- the Cotter Tens. If you’re new to RightStart, don’t worry -- this is a snap. Cotter Tens are all about powers of ten. You get to play around with really big numbers, like quadrillions. Kid1 is fascinated by really big numbers; I suspect this is common at this age.
Lesson 114 SImilar Triangles
Blessedly short, the point of this lesson is that two triangles are similar if two corresponding angles are equal. They may be different sizes, but they are similar.
It’s the sort of lesson that shows up on Are You Smarter Than a Fifth Grader (which should be re-done as Are You Smarter Than a Homeschool Mom, let’s face it).
Lesson 115 Gractions on the Multiplication Table
Another lesson with quick-to-complete worksheets. Kid1 did the worksheets in various colors of ink pens; she said the variety of colors helped her keep track of what she was doing (drawing squares around various boxes on the multiplication table).
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 111 Sierpinski Triangle
Introduces much history of geometry -- Euclid and the Elements, Benoit Mandelbrot and The Fractal Geometry of Nature, and , of course, Waclaw Sierpinski and The Sierpinski Triangle. I don’t know if Kid1 caught the point of all of this history -- I wouldn’t have at her age. Then again, she has a more subtle mind than I (this isn’t saying much).
The worksheets ask for three iterations of the Sierpinski Triangle.
Lesson 112 Koch Snowflake
We both hit a snag on worksheet 1. Kid1 is able to easily draw iterations of the Koch Snowflake, but the algorithm to figure out the perimeter escapes her. She is able to graph out what will happen to the permimeter and area -- the “analysis” section of the book pretty much lays that out -- but doesn’t get how to put the perimeters into numbers. I peek at the answers. I discover that each perimeter is to be multiplied by 4/3 to find the next iteration. Well, how the heck would I have known that? I’m totally clueless as to how we were supposed to figure that out. Really. The only thing I can think of is that the Sierpinski Triangle in lesson 111 had each iteration shaded 3/4 more, so maybe those numbers should’ve been on my mind? Huh? I should email RightStart and ask them.
Lesson 113 Cotter Tens Fractal
Yes, it’s the fractal we all know and love from Level B and/or Transitions -- the Cotter Tens. If you’re new to RightStart, don’t worry -- this is a snap. Cotter Tens are all about powers of ten. You get to play around with really big numbers, like quadrillions. Kid1 is fascinated by really big numbers; I suspect this is common at this age.
Lesson 114 SImilar Triangles
Blessedly short, the point of this lesson is that two triangles are similar if two corresponding angles are equal. They may be different sizes, but they are similar.
It’s the sort of lesson that shows up on Are You Smarter Than a Fifth Grader (which should be re-done as Are You Smarter Than a Homeschool Mom, let’s face it).
Lesson 115 Gractions on the Multiplication Table
Another lesson with quick-to-complete worksheets. Kid1 did the worksheets in various colors of ink pens; she said the variety of colors helped her keep track of what she was doing (drawing squares around various boxes on the multiplication table).
03 April 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 109 Tessellation Summary and Mondrian Art
Hurray! No tessellations to draw! Just a couple worksheet to summarize the types of tessellations, which can be filled out fairly quickly.
We can’t seem to connect with the website listed in the book for Mondrian Art. We have a couple of postcard size prints of Mondrian’s work, plus I found this website . The instructions are to draw a couple of Mondrian designs on the bottom of the worksheet; Kid1 uses a separate piece of paper which she mounts on construction paper for an artier effect.
Lesson 110 Box Fractals
I am asked, “Mommy, what’s 1/3 of 1/6?” I’m playing Corners with Kid2, and brush off the question, telling her to figure it out herself. I later discover that she ended up using a calculator and doing it in decimals. Yikes! I draw pictures on scrap paper to show how to figure it out.
“See, you end up with 6 groups of 3, which equals what? And here’s what the equation looks like ... remember this now?” This stuff was at the end of Level E. We even took time off from Geometry earlier this year and went back to review it. It isn’t sticking.
I notice that the lesson has a portion with a sidebar stating, “If you know all about exponents, you can skim this paragraph.” The glitch with multiplying fractions leaves me wondering whether she knows about exponents.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 109 Tessellation Summary and Mondrian Art
Hurray! No tessellations to draw! Just a couple worksheet to summarize the types of tessellations, which can be filled out fairly quickly.
We can’t seem to connect with the website listed in the book for Mondrian Art. We have a couple of postcard size prints of Mondrian’s work, plus I found this website . The instructions are to draw a couple of Mondrian designs on the bottom of the worksheet; Kid1 uses a separate piece of paper which she mounts on construction paper for an artier effect.
Lesson 110 Box Fractals
I am asked, “Mommy, what’s 1/3 of 1/6?” I’m playing Corners with Kid2, and brush off the question, telling her to figure it out herself. I later discover that she ended up using a calculator and doing it in decimals. Yikes! I draw pictures on scrap paper to show how to figure it out.
“See, you end up with 6 groups of 3, which equals what? And here’s what the equation looks like ... remember this now?” This stuff was at the end of Level E. We even took time off from Geometry earlier this year and went back to review it. It isn’t sticking.
I notice that the lesson has a portion with a sidebar stating, “If you know all about exponents, you can skim this paragraph.” The glitch with multiplying fractions leaves me wondering whether she knows about exponents.
28 March 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 106 Tessellating Triangles
As the title implies, this is all about tessellating with triangles. The drawing portion of worksheet 1 takes For. Ever. as Kid1 draws out jillions of tiny tessellating triangles with her drawing tools; I read aloud several chapters from a book as she works (I used to love listening to books when I was working on drafting projects, since it’s somewhat mindless work).
We pause for some whining about not understanding worksheet 2. I pick up the textbook and read it aloud, including the words “If you need a hint for the second worksheet...”blah blah blah. Oh, okay, now it makes sense. I am hopeful that Kid1 will eventually learn to re-read the lesson if she doesn’t instantly understand everything. Sigh.
Lesson 107 Tessellating Quadrilaterals
“Only 42 lessons until I’m finished with the book!”
I try to tell her that I think more lessons will be mailed out -- that the book isn’t completely written yet. My heart’s not in it, though.
And the lesson itself? Just more tessellations. Always more tessellations. “March 2007 -- Season of Tessellations” -- that’s how we’ll remember this time of our lives.
Lesson 108 Escher Tessellation
Hooray! I’ve been waiting for this lesson forever! We had a couple of books of Escher’s work that I used to spend hours and hours studying when I was in middle school. I requested some Escher books from the library, but they haven’t arrived yet (the books my family owns are apparently at my parents’ or a siblings’ house). I love this stuff.
The lesson also discusses the history of tessellations in various world cultures. A couple of Internet links are given which give examples, including this one that has some Escher.
The assignment is to make a tessellation with a more sinuous design, within the parameters of 4 corners. Kid1 isn’t happy with her results, feeling too constrained by the corners. Ah, the problems of designing/making art within someone else’s specifications ... it never ends, does it.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 106 Tessellating Triangles
As the title implies, this is all about tessellating with triangles. The drawing portion of worksheet 1 takes For. Ever. as Kid1 draws out jillions of tiny tessellating triangles with her drawing tools; I read aloud several chapters from a book as she works (I used to love listening to books when I was working on drafting projects, since it’s somewhat mindless work).
We pause for some whining about not understanding worksheet 2. I pick up the textbook and read it aloud, including the words “If you need a hint for the second worksheet...”blah blah blah. Oh, okay, now it makes sense. I am hopeful that Kid1 will eventually learn to re-read the lesson if she doesn’t instantly understand everything. Sigh.
Lesson 107 Tessellating Quadrilaterals
“Only 42 lessons until I’m finished with the book!”
I try to tell her that I think more lessons will be mailed out -- that the book isn’t completely written yet. My heart’s not in it, though.
And the lesson itself? Just more tessellations. Always more tessellations. “March 2007 -- Season of Tessellations” -- that’s how we’ll remember this time of our lives.
Lesson 108 Escher Tessellation
Hooray! I’ve been waiting for this lesson forever! We had a couple of books of Escher’s work that I used to spend hours and hours studying when I was in middle school. I requested some Escher books from the library, but they haven’t arrived yet (the books my family owns are apparently at my parents’ or a siblings’ house). I love this stuff.
The lesson also discusses the history of tessellations in various world cultures. A couple of Internet links are given which give examples, including this one that has some Escher.
The assignment is to make a tessellation with a more sinuous design, within the parameters of 4 corners. Kid1 isn’t happy with her results, feeling too constrained by the corners. Ah, the problems of designing/making art within someone else’s specifications ... it never ends, does it.
21 March 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 103 Pattern Unit
The smallest repeating of a tessellation is called a unit. Idea introduced in this lesson: a pattern has 3 elements -- a unit, repetition, and a system of organization.
The lesson involves identifying units, and also making translatons of the units. The first exercise looks like the brick pavers that are so popular in landscape applications.
Lesson 104 Dual Tessellations
By connecting the center of each polygon in a tessellation a new tessellation is formed. The student needs to remember how to find the center of a polygon to accomlish this. The lesson is easy, but takes a long time. It’s yet another lesson that can be done while listening to a book on tape.
Lesson 105 Tartan Plaids
The book has some discussion on the history of tartans, and also some information on weaving (the difference between a plain “tabby” weave and a twill weave). A suggestion is made to go look at some plaid fabric, which we have in abundance. The assignment is to design 3 plaids. This is incredibly easy.
By amazing coincidence, Weaver is posting pictures of her latest plaid weaving project today, so we get to look at a plaid on the loom. Kid1 is pretty sure we need to get a loom to further explore this idea.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 103 Pattern Unit
The smallest repeating of a tessellation is called a unit. Idea introduced in this lesson: a pattern has 3 elements -- a unit, repetition, and a system of organization.
The lesson involves identifying units, and also making translatons of the units. The first exercise looks like the brick pavers that are so popular in landscape applications.
Lesson 104 Dual Tessellations
By connecting the center of each polygon in a tessellation a new tessellation is formed. The student needs to remember how to find the center of a polygon to accomlish this. The lesson is easy, but takes a long time. It’s yet another lesson that can be done while listening to a book on tape.
Lesson 105 Tartan Plaids
The book has some discussion on the history of tartans, and also some information on weaving (the difference between a plain “tabby” weave and a twill weave). A suggestion is made to go look at some plaid fabric, which we have in abundance. The assignment is to design 3 plaids. This is incredibly easy.
By amazing coincidence, Weaver is posting pictures of her latest plaid weaving project today, so we get to look at a plaid on the loom. Kid1 is pretty sure we need to get a loom to further explore this idea.
13 March 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 101 Semiregular Tessellations
This is a 2-3 day lesson. It isn’t necessarily difficult, it just takes awhile to execute. It especially takes awhile when the weather suddenly becomes spring-like and we want to go outside for fresh air and sunshine.
Sidenote in the book: “If you’re finding pencil lines to be boring, here’s how to add some color to your work.” Oooh, perfect timing -- yes, it really is time to add some color. And now we have suggestions for how to use gel pens to draw tessellations. Cool.
Lesson 102 Demiregular Tessellations
What is the difference between a semiregular and demiregular tessellation? And how does the term semi-pure tessellation fit in to all of this?
Kid1 has realized that this somewhat mindless work of drawing out and coloring in tessellations can be done while listening to Jim Weiss reading Story of the World. Homeschool multi-tasking at its best! She even made extra photocopies of her tessellations so her younger sister could color some in; I think this is really clever on her part until I see that it is suggested in the book. Okay, then, it’s really clever on the author’s part. Kid2 is thrilled to be included in the “advanced math”.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 101 Semiregular Tessellations
This is a 2-3 day lesson. It isn’t necessarily difficult, it just takes awhile to execute. It especially takes awhile when the weather suddenly becomes spring-like and we want to go outside for fresh air and sunshine.
Sidenote in the book: “If you’re finding pencil lines to be boring, here’s how to add some color to your work.” Oooh, perfect timing -- yes, it really is time to add some color. And now we have suggestions for how to use gel pens to draw tessellations. Cool.
Lesson 102 Demiregular Tessellations
What is the difference between a semiregular and demiregular tessellation? And how does the term semi-pure tessellation fit in to all of this?
Kid1 has realized that this somewhat mindless work of drawing out and coloring in tessellations can be done while listening to Jim Weiss reading Story of the World. Homeschool multi-tasking at its best! She even made extra photocopies of her tessellations so her younger sister could color some in; I think this is really clever on her part until I see that it is suggested in the book. Okay, then, it’s really clever on the author’s part. Kid2 is thrilled to be included in the “advanced math”.
06 March 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 99 Two Pentagon Tessellations
“Start by cutting out the 25 pentagons on the first worksheet”. It is so hard to line up little bits of paper to make patterns. The edges curl, the little bits want to float away. Kid 1 tries putting double stick tape on them to help them stay in place, but that doesn’t work too well.
She is supposed to find 2 patterns she can make with these pentagons. She can only find one. I’m okay with that, given the little-bits-of-paper issue. She is supposed to draw the patterns on the worksheet. She opts (at my suggestion) to do the drawing freehand rather than with her drawing tools. Yes, the drawing tools can be more precise, but there is value in being able to draw geometric shapes freehand.
Lesson 100 Regular Tessellations
This lesson takes a look at 9-, 10- and 12-sided polygons. The student is to find the interior angle of various polygons, ranging from 3-sided to 12-sided. In our case, the student gets a quick refresher on how to find the interior angle (so did the student's mom, for that matter). She knew the interior angles of the smaller polygons off the top of her head, interestingly, but had to figure them out for the heptagon on up. Once that hurdle is leapt, the worksheet is fairly quick.
Again, the tessellations are drawn freehand at our house.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 99 Two Pentagon Tessellations
“Start by cutting out the 25 pentagons on the first worksheet”. It is so hard to line up little bits of paper to make patterns. The edges curl, the little bits want to float away. Kid 1 tries putting double stick tape on them to help them stay in place, but that doesn’t work too well.
She is supposed to find 2 patterns she can make with these pentagons. She can only find one. I’m okay with that, given the little-bits-of-paper issue. She is supposed to draw the patterns on the worksheet. She opts (at my suggestion) to do the drawing freehand rather than with her drawing tools. Yes, the drawing tools can be more precise, but there is value in being able to draw geometric shapes freehand.
Lesson 100 Regular Tessellations
This lesson takes a look at 9-, 10- and 12-sided polygons. The student is to find the interior angle of various polygons, ranging from 3-sided to 12-sided. In our case, the student gets a quick refresher on how to find the interior angle (so did the student's mom, for that matter). She knew the interior angles of the smaller polygons off the top of her head, interestingly, but had to figure them out for the heptagon on up. Once that hurdle is leapt, the worksheet is fairly quick.
Again, the tessellations are drawn freehand at our house.
20 February 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 97 Frieze Patterns
The goals of the lesson are to learn the terms used in frieze patterns, learn about the 7 types of frieze patterns, and to work with the patterns. Tangrams are used. It’s a simple concept, but takes a while to execute.
If I were a more with-it homeschooler, I would’ve tied this in to frieze patterns on ancient buildings, which would tie-in with all the reading about Greece and Rome we do daily. Cool idea, right? Too bad I didn’t think of it in time.
Lesson 98 Introduction to Tessellations
I’ve always thought tessellations were fun. We have a magnet set for making tessellations. We have wooden pattern blocks.
Kid1, on the other hand, asks if she could puh-leeeeeease do some other sort of math, anything but geometry, which has apparently become insufferably boring. Perhaps it’s tessellation burnout. I suggest she just Get It Over With, since she’ll have to do it eventually.
She does. It turns out to be a quick lesson. I don’t know if she realized the next 6 lessons are also on tessellations, though.
The next lesson shows a tiling pattern from ancient Egypt. Aha. My chance to redeem myself and tie this in to a favorite history subject. Must go google some historical tessellations.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 97 Frieze Patterns
The goals of the lesson are to learn the terms used in frieze patterns, learn about the 7 types of frieze patterns, and to work with the patterns. Tangrams are used. It’s a simple concept, but takes a while to execute.
If I were a more with-it homeschooler, I would’ve tied this in to frieze patterns on ancient buildings, which would tie-in with all the reading about Greece and Rome we do daily. Cool idea, right? Too bad I didn’t think of it in time.
Lesson 98 Introduction to Tessellations
I’ve always thought tessellations were fun. We have a magnet set for making tessellations. We have wooden pattern blocks.
Kid1, on the other hand, asks if she could puh-leeeeeease do some other sort of math, anything but geometry, which has apparently become insufferably boring. Perhaps it’s tessellation burnout. I suggest she just Get It Over With, since she’ll have to do it eventually.
She does. It turns out to be a quick lesson. I don’t know if she realized the next 6 lessons are also on tessellations, though.
The next lesson shows a tiling pattern from ancient Egypt. Aha. My chance to redeem myself and tie this in to a favorite history subject. Must go google some historical tessellations.
06 February 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 93 Angles of Incidence and Reflection
Okay, this was a really cool lesson. It’s sort of like that thing you did back in school when your teacher shone a strobe light on an air hockey table and you shot the puck around the table and watched the patterns it made -- remember that?
You pretend to shoot a pool ball, draw the angle of reflection when it hits the side of the table, find where it will next hit, find the next reflection, draw the trajectory, etc. etc. until the ball finally goes in the pocket. At the bottom of the page of the math book is an Internet link that I can’t get to work; I think this is the link they meant to put there.
Lesson 94 Lines of Symmetry
Kid1 feels there is a mistake in the answer sheet. She is filling in a chart that asks for the maximum number of lines of symmetry for a rhombus; she feels the answer should be 4, just as it was for the square, since, “well, Mommy, a square is a type of rhombus, you know, and they’re asking for the maximum.” I can’t find this on the errata lists, but the errata lists aren’t in lesson number order (which is really, really annoying, let me tell you).
I look at her worksheet later, and discover that she’s written “I’m right” in flourescent pink ink next to her answer.
The lesson introduces the sign for infinity. This holds no mystery for Kid1, possibly due to our School House Rock DVDs, in which Figure 8 is one of my absolute favorite songs.
Lesson 95 Rotation Symmetry
Another misprint: this time the text reads, “in the center figure above...” when there is no center figure. However, this one I can find in the errata. Of course, I don’t find it until the next day, mostly because that’s when I finally got around to looking for it. Kid1 is able to complete the assignment having never seen it.
Lesson 96 Symmetry Connections
This lesson consolidates the previous lessons on symmetry. The student looks for line symmetry, point symmetry, and rotational symmetry in several shapes and figures, also noting degrees of rotation. A fairly quick lesson, given that there’s not much drawing.
I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.
RightStart Geometry:
Lesson 93 Angles of Incidence and Reflection
Okay, this was a really cool lesson. It’s sort of like that thing you did back in school when your teacher shone a strobe light on an air hockey table and you shot the puck around the table and watched the patterns it made -- remember that?
You pretend to shoot a pool ball, draw the angle of reflection when it hits the side of the table, find where it will next hit, find the next reflection, draw the trajectory, etc. etc. until the ball finally goes in the pocket. At the bottom of the page of the math book is an Internet link that I can’t get to work; I think this is the link they meant to put there.
Lesson 94 Lines of Symmetry
Kid1 feels there is a mistake in the answer sheet. She is filling in a chart that asks for the maximum number of lines of symmetry for a rhombus; she feels the answer should be 4, just as it was for the square, since, “well, Mommy, a square is a type of rhombus, you know, and they’re asking for the maximum.” I can’t find this on the errata lists, but the errata lists aren’t in lesson number order (which is really, really annoying, let me tell you).
I look at her worksheet later, and discover that she’s written “I’m right” in flourescent pink ink next to her answer.
The lesson introduces the sign for infinity. This holds no mystery for Kid1, possibly due to our School House Rock DVDs, in which Figure 8 is one of my absolute favorite songs.
Lesson 95 Rotation Symmetry
Another misprint: this time the text reads, “in the center figure above...” when there is no center figure. However, this one I can find in the errata. Of course, I don’t find it until the next day, mostly because that’s when I finally got around to looking for it. Kid1 is able to complete the assignment having never seen it.
Lesson 96 Symmetry Connections
This lesson consolidates the previous lessons on symmetry. The student looks for line symmetry, point symmetry, and rotational symmetry in several shapes and figures, also noting degrees of rotation. A fairly quick lesson, given that there’s not much drawing.
17 January 2007
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
On Tuesdays I upload an update of what we did in math for the week.
RightStart Geometry:
Lesson 85 making Wheel Designs
As it says in the book, this is similar to Lesson 114 in Level E. Kid1 noticed some nuance of variation.
Lesson 86 Identifying Relfections and Rotations
We are hitting a segment of lessons which are done quietly, with a simple, “well, that was easy,” as the books are reshelved. Really, I don’t have much to say except that they’re easy. If math is a struggle, look to this segment as a breather.
Lesson 87 Translations
“Translation is the mathematical name for slide.” Still in the easy segment, folks.
Lesson 88 Transformations
The worksheet reminds me of something out of a book of drawing lessons, but Kid1 comments that if it were drawing the figures would be slightly flattened (due to perspective and vanishing points, although she doesn’t use those words).
The materials list leaves out a couple of items the student will need. Other than than, very straight forward.
Lesson 89 Double Reflections
The only reason she isn’t flying through these lessons is that she’s taken to reading comic books on the side while she’s working them.
Lesson 90 Finding the Line of Reflection
Worksheet question: “Connect each point of the triangle with its corresponding image using a dotted line. Then construct the perpendicular bisector of each line. What do you observe?” Answer I find written on worksheet: “That this is a lot easier and more fun than I thought it would be.” Verbal comment: “It’s so obvious that it’s going to be the line of reflection that it isn’t worth saying that.”
On Tuesdays I upload an update of what we did in math for the week.
RightStart Geometry:
Lesson 85 making Wheel Designs
As it says in the book, this is similar to Lesson 114 in Level E. Kid1 noticed some nuance of variation.
Lesson 86 Identifying Relfections and Rotations
We are hitting a segment of lessons which are done quietly, with a simple, “well, that was easy,” as the books are reshelved. Really, I don’t have much to say except that they’re easy. If math is a struggle, look to this segment as a breather.
Lesson 87 Translations
“Translation is the mathematical name for slide.” Still in the easy segment, folks.
Lesson 88 Transformations
The worksheet reminds me of something out of a book of drawing lessons, but Kid1 comments that if it were drawing the figures would be slightly flattened (due to perspective and vanishing points, although she doesn’t use those words).
The materials list leaves out a couple of items the student will need. Other than than, very straight forward.
Lesson 89 Double Reflections
The only reason she isn’t flying through these lessons is that she’s taken to reading comic books on the side while she’s working them.
Lesson 90 Finding the Line of Reflection
Worksheet question: “Connect each point of the triangle with its corresponding image using a dotted line. Then construct the perpendicular bisector of each line. What do you observe?” Answer I find written on worksheet: “That this is a lot easier and more fun than I thought it would be.” Verbal comment: “It’s so obvious that it’s going to be the line of reflection that it isn’t worth saying that.”
19 December 2006
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
On Tuesdays I upload an update of what we did in math for the week.
RightStart Geometry:
Lesson 84 Rotating
The lesson explains what rotation means in a mathematical sense, then has the student draw various rotations.
On one hand, the directions say to “measure only the 2.5 cm line,” deriving the rest of the lines and angles from your knowledge of how to draw geometric figures. On the other hand, the directions say to “construct every line accurately. Don’t guess.” Well. Tears of frustration ensue during the final rotation, which for some reason is wonky. I know the feeling from various projects I’ve done.
I am not allowed to help. I think she’s caught on that it takes me awhile to get up to speed on these lessons, as she’s journeying to places I either haven’t been for a long time, or perhaps never visited before. It occurs to me that it would’ve been a good idea to go through all the lessons myself a bit ahead of her.
On Tuesdays I upload an update of what we did in math for the week.
RightStart Geometry:
Lesson 84 Rotating
The lesson explains what rotation means in a mathematical sense, then has the student draw various rotations.
On one hand, the directions say to “measure only the 2.5 cm line,” deriving the rest of the lines and angles from your knowledge of how to draw geometric figures. On the other hand, the directions say to “construct every line accurately. Don’t guess.” Well. Tears of frustration ensue during the final rotation, which for some reason is wonky. I know the feeling from various projects I’ve done.
I am not allowed to help. I think she’s caught on that it takes me awhile to get up to speed on these lessons, as she’s journeying to places I either haven’t been for a long time, or perhaps never visited before. It occurs to me that it would’ve been a good idea to go through all the lessons myself a bit ahead of her.
05 December 2006
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
On Tuesdays I upload an update of what we did in math for the week.
RightStart Geometry:
Lesson 83 Reflecting
This lesson zips by quickly and painlessly. We do not have the optional Reflecta or Mira or GeoReflector. I suspect that Kid1 was able to visualize what would happen if she had used them.
Frankly, my only contact with the material is hearing Kid1 tell Kid2 that it’s an easy lesson. The drawing portion is much quicker than the tangrams of earlier lessons.
On Tuesdays I upload an update of what we did in math for the week.
RightStart Geometry:
Lesson 83 Reflecting
This lesson zips by quickly and painlessly. We do not have the optional Reflecta or Mira or GeoReflector. I suspect that Kid1 was able to visualize what would happen if she had used them.
Frankly, my only contact with the material is hearing Kid1 tell Kid2 that it’s an easy lesson. The drawing portion is much quicker than the tangrams of earlier lessons.
21 November 2006
RightStart Geometry
The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.
On Tuesdays I upload an update of what we did in math for the week.
RightStart Geometry:
Leson 80 Pizza Problems
The lesson looks at unit costs. It also looks at ordering pizza based on cost per square inch. Of course, this is a silly way to order pizza, since no one eats it by the inch. Better to figure the price per slice, taking into account the relative thickness of the crust and how generous the restaurant is with the toppings. But I suppose it makes for a fun worksheet.
Lesson 81 Revisiting Tangrams
We love tangrams, and have 2 sets of plastic ones. These problems are simple, yet tedious in that the student needs to draw the various parts of the tangram set. It is much easier to work through the lesson with plastic tangrams, by the way, instead of copying of the shapes onto cardstock and then trying to manipulate the cardstock tangrams.
The second worksheet shows shapes, then asks for several ways to form each shape. The answers on the answer sheet are not exhaustive by any means. I notice Kid1 struggling to come up with a final solution for the pentagon. I pause while passing by and say, “Why don’t you try this?” While she protests, “Mommy, that’s not going to work!” I come up with 2 more solutions (MrV has told me if I ever need to re-enter the workforce I should consider package engineering).
At the end of the worksheet, the student is asked which shapes cover the greatest area. The answer is based on the tangram shapes used to make the various shapes shown. Fun lesson!
Lesson 82 Aligning Objects
Working again with the shapes of the tangrams, this time learning to align right, align left, align top, and align bottom. It’s an easy concept, but all the drawing is very tedious. I suggest to Kid1 she split it up over a couple of days, since it takes over an hour.
On Tuesdays I upload an update of what we did in math for the week.
RightStart Geometry:
Leson 80 Pizza Problems
The lesson looks at unit costs. It also looks at ordering pizza based on cost per square inch. Of course, this is a silly way to order pizza, since no one eats it by the inch. Better to figure the price per slice, taking into account the relative thickness of the crust and how generous the restaurant is with the toppings. But I suppose it makes for a fun worksheet.
Lesson 81 Revisiting Tangrams
We love tangrams, and have 2 sets of plastic ones. These problems are simple, yet tedious in that the student needs to draw the various parts of the tangram set. It is much easier to work through the lesson with plastic tangrams, by the way, instead of copying of the shapes onto cardstock and then trying to manipulate the cardstock tangrams.
The second worksheet shows shapes, then asks for several ways to form each shape. The answers on the answer sheet are not exhaustive by any means. I notice Kid1 struggling to come up with a final solution for the pentagon. I pause while passing by and say, “Why don’t you try this?” While she protests, “Mommy, that’s not going to work!” I come up with 2 more solutions (MrV has told me if I ever need to re-enter the workforce I should consider package engineering).
At the end of the worksheet, the student is asked which shapes cover the greatest area. The answer is based on the tangram shapes used to make the various shapes shown. Fun lesson!
Lesson 82 Aligning Objects
Working again with the shapes of the tangrams, this time learning to align right, align left, align top, and align bottom. It’s an easy concept, but all the drawing is very tedious. I suggest to Kid1 she split it up over a couple of days, since it takes over an hour.
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